The main intention of this paper is to deal with the weak singularity of solutions to some nonlinear Hadamard type fractional differential systems (HTFDSs) which could be viewed as the generalization of classic Hadamard fractional settings. Resorting to the lower and upper solutions technique and constructing the compatible weighted Banach space, the completely continuous operator described by Hadamard type fractional versions as well as a sufficient criterion for the existence of blow-up solutions to some nonlinear HTFDSs is established. Additionally, the comparative analysis on the blow-up rate affected by critical system parameters is also presented, and several examples clearly illustrate the effectiveness and efficiency of the proposed results.

本文的主要目的是处理一些非线性 Hadamard 型分数微分系统 (HTFDS) 解的弱奇异性，这可以看作是经典 Hadamard 分数设置的推广。借助上下解技术，构造兼容的加权Banach空间，建立了Hadamard型分数版本描述的完全连续算子，以及一些非线性HTFDS存在爆破解的充分判据。此外，还对受关键系统参数影响的爆破率进行了比较分析，并通过几个例子清楚地说明了所提出结果的有效性和效率。